Question: Simplify the expression. $(-4r^{4}-r^{3}+4r)(3r^{4}+2r^{3})$
Explanation: First use the distributive property. $ - 4 r^4 (3 r^4) - 4 r^4 (2 r^3) - r^3 (3 r^4) - r^3 (2 r^3) + 4 r (3 r^4) + 4 r (2 r^3) $ Simplify. $ - 12r^{8} - 8r^{7} - 3r^{7} - 2r^{6} + 12r^{5} + 8r^{4} $ $-12r^{8}-11r^{7}-2r^{6}+12r^{5}+8r^{4}$ Identify like terms. $ {- 12r^{8}} {- 8r^{7}} {- 3r^{7}} {- 2r^{6}} {+ 12r^{5}} {+ 8r^{4}} $ Add the coefficients. $ { -12r^{8}} { -11r^{7}} { -2r^{6}} {+ 12r^{5}} {+ 8r^{4}} $